4 Answers
4

The first number specifies the quantity of digits of the set above it and the second number specifies what the digit is. The second line is 11 it is saying that the line above it is one one. The third line states that the line above it is two ones. The fourth line is saying there is one two and one one.

$\begingroup$There you go :) thats the fun (and embarrassment) of interacting with intellectuals like you @Doorknob$\endgroup$
– skvSep 17 '14 at 14:03

3

$\begingroup$Bonus points: Will a four ever occur, and how would you prove that?$\endgroup$
– Mooing DuckSep 17 '14 at 23:23

$\begingroup$@MooingDuck there's a bit more info on this at A005150 in The On-Line Encyclopedia of Integer Sequences.$\endgroup$
– user2322Sep 18 '14 at 1:15

5

$\begingroup$You can never have a four, as this would imply that the previous line contained four of the same digit in a row, which in turn implies you've described the line before that incorrectly (1111 = "one 1 then one 1", which would actually be described as "21" or "two 1s"$\endgroup$
– IanF1Jan 3 '15 at 19:19

Using similar rules as the accept answer. The first number specified the quantity of digits of the entire set above it and the second number specifies what the digit is. The accepted answer is a reading of the prior sequence, this answer is a summary of the prior sequence.

Fun fact, coming back to this. This sequence will hit a point where it will output the same number forever.

$\begingroup$Why is the next number 1231 and not 3112? I would think you order the pairs in the order of first appearance. This appears to be in descending order of the digit being counted.$\endgroup$
– TheRubberDuckSep 17 '14 at 18:27

4

$\begingroup$It could be either way, really. The OP was a little vague, so there will be multiple answers.$\endgroup$
– drovaniSep 17 '14 at 19:03

The first number specifies the quantity of digits of the set above it and the second number specifies what the digit is. The second line is 11 it is saying that the line above it is one one. The third line states that the line above it is two ones. The fourth line is saying there is one two and one one.